x^2+(9/16)x=2.5

Solution for x^2+(9/16)x=2.5 equation:

x^2+(9/16)x=2.5

We move all terms to the left:

x^2+(9/16)x-(2.5)=0


Domain of the equation: 16)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2+(+9/16)x-(2.5)=0

We add all the numbers together, and all the variables

x^2+(+9/16)x-2.5=0

We multiply parentheses

x^2+9x^2-2.5=0

We add all the numbers together, and all the variables

10x^2-2.5=0

a = 10; b = 0; c = -2.5;
Δ = b2-4ac
Δ = 02-4·10·(-2.5)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*10}=\frac{-10}{20}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*10}=\frac{10}{20}
=1/2
$